Math Problem Statement
Determine whether the system of equations shown in the graph has no solution or infinitely many solutions. The two lines are ______, so the system of equations has ______.
Solution
The question is asking whether the system of equations shown in the graph has no solution or infinitely many solutions.
Looking at the image:
- The two lines appear to be parallel. This is indicated by the fact that they never intersect.
- For a system of linear equations, if two lines are parallel, they have the same slope but different y-intercepts, meaning they will never intersect.
- A system with parallel lines has no solution because there is no point that satisfies both equations simultaneously.
So, the correct answers are:
- The two lines are parallel.
- The system of equations has no solution.
Would you like more details or have any questions?
Here are some related questions:
- What does it mean when two lines have infinitely many solutions?
- How can you tell if two lines are parallel just by looking at their equations?
- What is the slope-intercept form of a linear equation, and how does it help in identifying parallel lines?
- What types of systems of equations have exactly one solution?
- Can non-linear systems of equations also have no solution?
Tip: Remember, parallel lines always have the same slope but different y-intercepts.
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Math Problem Analysis
Mathematical Concepts
Linear Systems
Parallel Lines
Formulas
Slope formula
Equation of a line
Theorems
If two lines are parallel, they have no solutions.
Suitable Grade Level
Grade 8-10